OntoMetrics - User contributions [en]

Schema Metrics

2016-09-07T14:48:03Z

Bl137: /* Class Relation Ratio */

Schema metrics address the design of the ontology. Although we cannot definitely know if the ontology design correctly models the domain knowledge, metrics in this category indicate the richness, width, depth, and inheritance of an ontology schema design. The most significant metrics in this category are described next.

==Attribute Richness==
The number of attributes (slots) that are defined for each class can indicate both the quality of ontology design and the amount of information pertaining to instance data. In general we assume that the more slots that are defined the more knowledge the ontology conveys.

The '''attribute richness (AR)''' is defined as the average number of attributes (slots) per class. It is computed as the '''number attributes for all classes (att)''' divided by the '''number of classes (C)'''.

<math>AR = \dfrac{|ATT|}{|C|}</math>

Note: Usually, only the functional attributes are counted to calculate this metric, as stated in the OWL definition. In our metric calculation, we omit this restriction and use all declared attributes to calculate, because not many modellers use the possibility of defining functional attributes. Also, the datatype are being handled as attributes as well.

[[Schema_Metrics#Sources | Source 1]]

==Inheritance Richness==

'''Inheritance Richness (IR)''' measure describes the distribution of information across different levels of the ontology’s inheritance tree or the fan-out of parent classes. This is a good indication of how well knowledge is grouped into different categories and subcategories in the ontology. This measure can distinguish a horizontal ontology (where classes have a large number of direct subclasses) from a vertical ontology (where classes have a small number of direct subclasses). An ontology with a low inheritance richness would be of a deep (or vertical) ontology, which indicates that the ontology covers a specific domain in a detailed manner, while an ontology with a high IR would be a shallow (or horizontal) ontology, which indicates that the ontology represents a wide range of general knowledge with a low level of detail.

The inheritance richness of the schema (IR) is defined as the average number of subclasses per class.
The number of subclasses of a class is defined as <math> |H^C(C_1,C_i)|</math>. '''H''' is the '''number of inheritance relationships'''.

<math>IR = \frac{\sum_{C_i \in C}|H^C(C_1,C_i)|}{|C|}</math>

[[Schema_Metrics#Sources | Source 1]]

==Relationship Richness==

This metric reflects the diversity of the types of relations in the ontology. An ontology that contains only inheritance relationships usually conveys less information than an ontology that contains a diverse set of relationships. The relationship richness is represented as the percentage of the (non-inheritance) relationships between classes compared to all of the possible connections that can include inheritance and non-inheritance relationships.

The '''relationship richness (RR)''' of a schema is defined as the ratio of the '''number of (non-inheritance) relationships (P)''', divided by the '''total number of relationships''' defined in the schema (the sum of the '''number of inheritance relationships (H)''' and '''non-inheritance relationships (P)''').

<math>RR = \frac{|P|}{|H|+|P|}</math>

Note: The following relationships are being counted as non-inherited relationships:

Object Properties,

Equivalent Classes,

Disjoint Classes.

The subclasses (Subclasses of) are being handled as inheritance relationships.

[[Schema_Metrics#Sources | Source 1]]

==Axiom Class Ratio==

This metric describes the ratio between axioms and classes. It is calculated as the average amount of axioms per class.
<math>Axiom class ratio=\frac{Axioms}{Classes}</math>

[[Schema_Metrics#Sources | Source 2]]

==Inverse Relations Ratio==

This metric describes the ratio between the inverse relations and all relations.
It is calculated as follows:
<math>Inverse Relations Ratio = \frac{Inverse Object Properties + Inverse Functional Data Properties}{All Object Properties + All Functional Data Properties}</math>

[[Schema_Metrics#Sources | Source 2]]

==Class Relation Ratio==

This metric describes the ratio between the classes and the relations in the ontology.
<math>Class Relation Ratio =\frac{Classes}{Relationships}</math>

The following ontology components are counted as relationships:
Object Properties,

Equivalent Classes,

Disjoint Classes,

Subclasses(Subclass of).

[[Schema_Metrics#Sources | Source 2]]

==Attribute-Class Ratio==

This metric represents the relation between the classes containing attributes and all classes. The difference to attribute richness is that not the amount of attributes is counted. It is only counted whether a class has attributes or not.

<math>AttributeClass Ratio=\frac{Classes With Attributes}{Number Of Classes}</math>

==Equivalence Ratio==

This metric calculates the ratio between similar classes and all classes in the ontology.

It is being calculated as follows:
<math>Equivalence Ratio =\frac{Same Classes}{Number Of All Classes}</math>

==Sources==

#''Samir Tartir, I. Budak Arpinar, Amit P. Sheth: Ontological Evaluation and Validation In: Theory and Applications of Ontology: Computer Applications 2010, pp 115-130. http://link.springer.com/chapter/10.1007%2F978-90-481-8847-5_5''
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005, pp 19-20. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf

Schema Metrics

2016-09-07T14:20:03Z

Bl137: /* Relationship Richness */

Schema metrics address the design of the ontology. Although we cannot definitely know if the ontology design correctly models the domain knowledge, metrics in this category indicate the richness, width, depth, and inheritance of an ontology schema design. The most significant metrics in this category are described next.

==Attribute Richness==
The number of attributes (slots) that are defined for each class can indicate both the quality of ontology design and the amount of information pertaining to instance data. In general we assume that the more slots that are defined the more knowledge the ontology conveys.

The '''attribute richness (AR)''' is defined as the average number of attributes (slots) per class. It is computed as the '''number attributes for all classes (att)''' divided by the '''number of classes (C)'''.

<math>AR = \dfrac{|ATT|}{|C|}</math>

Note: Usually, only the functional attributes are counted to calculate this metric, as stated in the OWL definition. In our metric calculation, we omit this restriction and use all declared attributes to calculate, because not many modellers use the possibility of defining functional attributes. Also, the datatype are being handled as attributes as well.

[[Schema_Metrics#Sources | Source 1]]

==Inheritance Richness==

'''Inheritance Richness (IR)''' measure describes the distribution of information across different levels of the ontology’s inheritance tree or the fan-out of parent classes. This is a good indication of how well knowledge is grouped into different categories and subcategories in the ontology. This measure can distinguish a horizontal ontology (where classes have a large number of direct subclasses) from a vertical ontology (where classes have a small number of direct subclasses). An ontology with a low inheritance richness would be of a deep (or vertical) ontology, which indicates that the ontology covers a specific domain in a detailed manner, while an ontology with a high IR would be a shallow (or horizontal) ontology, which indicates that the ontology represents a wide range of general knowledge with a low level of detail.

The inheritance richness of the schema (IR) is defined as the average number of subclasses per class.
The number of subclasses of a class is defined as <math> |H^C(C_1,C_i)|</math>. '''H''' is the '''number of inheritance relationships'''.

<math>IR = \frac{\sum_{C_i \in C}|H^C(C_1,C_i)|}{|C|}</math>

[[Schema_Metrics#Sources | Source 1]]

==Relationship Richness==

This metric reflects the diversity of the types of relations in the ontology. An ontology that contains only inheritance relationships usually conveys less information than an ontology that contains a diverse set of relationships. The relationship richness is represented as the percentage of the (non-inheritance) relationships between classes compared to all of the possible connections that can include inheritance and non-inheritance relationships.

The '''relationship richness (RR)''' of a schema is defined as the ratio of the '''number of (non-inheritance) relationships (P)''', divided by the '''total number of relationships''' defined in the schema (the sum of the '''number of inheritance relationships (H)''' and '''non-inheritance relationships (P)''').

<math>RR = \frac{|P|}{|H|+|P|}</math>

Note: The following relationships are being counted as non-inherited relationships:

Object Properties,

Equivalent Classes,

Disjoint Classes.

The subclasses (Subclasses of) are being handled as inheritance relationships.

[[Schema_Metrics#Sources | Source 1]]

==Axiom Class Ratio==

This metric describes the ratio between axioms and classes. It is calculated as the average amount of axioms per class.
<math>Axiom class ratio=\frac{Axioms}{Classes}</math>

[[Schema_Metrics#Sources | Source 2]]

==Inverse Relations Ratio==

This metric describes the ratio between the inverse relations and all relations.
It is calculated as follows:
<math>Inverse Relations Ratio = \frac{Inverse Object Properties + Inverse Functional Data Properties}{All Object Properties + All Functional Data Properties}</math>

[[Schema_Metrics#Sources | Source 2]]

==Class Relation Ratio==

This metric describes the ratio between the classes and the relations in the ontology.
<math>Class Relation Ratio =\frac{Classes}{Relationships}</math>

The following ontology components are counted as relationships:
Object Properties,

Equivalent Classes,

Disjoint Classes,

Class Assertion,

Same individuals,

Different individuals,

Subclasses(Subclass of).

[[Schema_Metrics#Sources | Source 2]]

==Attribute-Class Ratio==

This metric represents the relation between the classes containing attributes and all classes. The difference to attribute richness is that not the amount of attributes is counted. It is only counted whether a class has attributes or not.

<math>AttributeClass Ratio=\frac{Classes With Attributes}{Number Of Classes}</math>

==Equivalence Ratio==

This metric calculates the ratio between similar classes and all classes in the ontology.

It is being calculated as follows:
<math>Equivalence Ratio =\frac{Same Classes}{Number Of All Classes}</math>

==Sources==

#''Samir Tartir, I. Budak Arpinar, Amit P. Sheth: Ontological Evaluation and Validation In: Theory and Applications of Ontology: Computer Applications 2010, pp 115-130. http://link.springer.com/chapter/10.1007%2F978-90-481-8847-5_5''
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005, pp 19-20. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf

Schema Metrics

2016-09-07T14:19:48Z

Bl137: /* Relationship Richness */

Schema metrics address the design of the ontology. Although we cannot definitely know if the ontology design correctly models the domain knowledge, metrics in this category indicate the richness, width, depth, and inheritance of an ontology schema design. The most significant metrics in this category are described next.

==Attribute Richness==
The number of attributes (slots) that are defined for each class can indicate both the quality of ontology design and the amount of information pertaining to instance data. In general we assume that the more slots that are defined the more knowledge the ontology conveys.

The '''attribute richness (AR)''' is defined as the average number of attributes (slots) per class. It is computed as the '''number attributes for all classes (att)''' divided by the '''number of classes (C)'''.

<math>AR = \dfrac{|ATT|}{|C|}</math>

Note: Usually, only the functional attributes are counted to calculate this metric, as stated in the OWL definition. In our metric calculation, we omit this restriction and use all declared attributes to calculate, because not many modellers use the possibility of defining functional attributes. Also, the datatype are being handled as attributes as well.

[[Schema_Metrics#Sources | Source 1]]

==Inheritance Richness==

'''Inheritance Richness (IR)''' measure describes the distribution of information across different levels of the ontology’s inheritance tree or the fan-out of parent classes. This is a good indication of how well knowledge is grouped into different categories and subcategories in the ontology. This measure can distinguish a horizontal ontology (where classes have a large number of direct subclasses) from a vertical ontology (where classes have a small number of direct subclasses). An ontology with a low inheritance richness would be of a deep (or vertical) ontology, which indicates that the ontology covers a specific domain in a detailed manner, while an ontology with a high IR would be a shallow (or horizontal) ontology, which indicates that the ontology represents a wide range of general knowledge with a low level of detail.

The inheritance richness of the schema (IR) is defined as the average number of subclasses per class.
The number of subclasses of a class is defined as <math> |H^C(C_1,C_i)|</math>. '''H''' is the '''number of inheritance relationships'''.

<math>IR = \frac{\sum_{C_i \in C}|H^C(C_1,C_i)|}{|C|}</math>

[[Schema_Metrics#Sources | Source 1]]

==Relationship Richness==

This metric reflects the diversity of the types of relations in the ontology. An ontology that contains only inheritance relationships usually conveys less information than an ontology that contains a diverse set of relationships. The relationship richness is represented as the percentage of the (non-inheritance) relationships between classes compared to all of the possible connections that can include inheritance and non-inheritance relationships.

The '''relationship richness (RR)''' of a schema is defined as the ratio of the '''number of (non-inheritance) relationships (P)''', divided by the '''total number of relationships''' defined in the schema (the sum of the '''number of inheritance relationships (H)''' and '''non-inheritance relationships (P)''').

<math>RR = \frac{|P|}{|H|+|P|}</math>

Note: The following relationships are being counted as non-inherited relationships:

Object Properties,

Equivalent Classes,

Disjoint Classes,

The subclasses (Subclasses of) are being handled as inheritance relationships.

[[Schema_Metrics#Sources | Source 1]]

==Axiom Class Ratio==

This metric describes the ratio between axioms and classes. It is calculated as the average amount of axioms per class.
<math>Axiom class ratio=\frac{Axioms}{Classes}</math>

[[Schema_Metrics#Sources | Source 2]]

==Inverse Relations Ratio==

This metric describes the ratio between the inverse relations and all relations.
It is calculated as follows:
<math>Inverse Relations Ratio = \frac{Inverse Object Properties + Inverse Functional Data Properties}{All Object Properties + All Functional Data Properties}</math>

[[Schema_Metrics#Sources | Source 2]]

==Class Relation Ratio==

This metric describes the ratio between the classes and the relations in the ontology.
<math>Class Relation Ratio =\frac{Classes}{Relationships}</math>

The following ontology components are counted as relationships:
Object Properties,

Equivalent Classes,

Disjoint Classes,

Class Assertion,

Same individuals,

Different individuals,

Subclasses(Subclass of).

[[Schema_Metrics#Sources | Source 2]]

==Attribute-Class Ratio==

This metric represents the relation between the classes containing attributes and all classes. The difference to attribute richness is that not the amount of attributes is counted. It is only counted whether a class has attributes or not.

<math>AttributeClass Ratio=\frac{Classes With Attributes}{Number Of Classes}</math>

==Equivalence Ratio==

This metric calculates the ratio between similar classes and all classes in the ontology.

It is being calculated as follows:
<math>Equivalence Ratio =\frac{Same Classes}{Number Of All Classes}</math>

==Sources==

#''Samir Tartir, I. Budak Arpinar, Amit P. Sheth: Ontological Evaluation and Validation In: Theory and Applications of Ontology: Computer Applications 2010, pp 115-130. http://link.springer.com/chapter/10.1007%2F978-90-481-8847-5_5''
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005, pp 19-20. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf

Knowledgebase Metrics

2016-09-07T10:35:22Z

Bl137:

The way data is placed within an ontology is also a very important measure of ontology quality because it can indicate the effectiveness of the ontology design and the amount of real-world knowledge represented by the ontology. Instance metrics include metrics that describe the knowledgebase as a whole, and metrics that describe the way each schema class is being utilized in the knowledgebase.

==Average Population==

(The average distribution of instances across all classes)

This measure is an indication of the number of instances compared to the number of classes. It can be useful if the ontology developer is not sure if enough instances were extracted compared to the number of classes.

Formally, the '''average population (AP)''' of classes in a knowledgebase is defined as the '''number of instances of the knowledgebase (I)''' divided by the '''number of classes defined in the ontology schema (C)'''.
<math>AP=\frac{|I|}{|C|}</math>

The result will be a real number that shows how well is the data extraction process that was performed to populate the knowledgebase. For example, if the average number of instances per class is low, when read in conjunction with the previous metric, this number would indicate that the instances extracted into the knowledgebase might be insufficient to represent all of the knowledge in the schema. Keep in mind that some of the schema classes might have a very low number or a very high number by the nature of what it is representing.

[[Knowledgebase_Metrics#Sources | Source 1]]

==Class Richness==

This metric is related to how instances are distributed across classes. The number of classes that have instances in the knowledgebase is compared with the total number of classes, giving a general idea of how well the knowledgebase utilizes the knowledge modelled by the schema classes. Thus, if the knowledgebase has a very low Class Richness, then the knowledgebase does not have data that exemplifies all the class knowledge that exists in the schema. On the other hand, a knowledgebase that has a very high class richness would indicate that the data in the knowledgebase represents most of the knowledge in the schema.

The '''class richness (CR)''' of a knowledgebase is defined as the percentage of the '''number of non-empty classes (classes with instances) (C')''' divided by the '''total number of classes (C)''' defined in the ontology schema.

<math>CR= \frac{|C'|}{|C|}</math>

[[Knowledgebase_Metrics#Sources | Source 1]]

==Cohesion==

The cohesion shows the degree of relatedness between the different entities. When the entities of an ontology are highly related there is a strong cohesion value.

To be able to measure the cohesion three different metrics will be used:

===Number of root classes (NoR)===
'''Same as Absolute Root Cardinality in Graph Metrics!!!'''

Displays the number of root classes of an ontology, a root class is a class which is not a sub class of any other class in the ontology. <math> C_j</math> is the jth root class.
<math>NoR= \sum C_j </math> ''for all'' <math>1 \le j \le n</math>
===Number of leaf classes (NoL)===
'''Same as Absolute Leaf Cardinality in Graph Metrics!!!'''

Displays the number of leaf classes of an ontology, a leaf class doesn't have any sub classes. <math> L_j</math> is the jth leaf class.

<math>NoL= \sum L_j </math> ''for all'' <math>1 \le j \le n</math>
===Average depth of inheritance tree of leaf nodes (ADIT-LN)===
'''Same as Average Depth in Graph Metrics!!!'''

It is the sum of the depth of all paths divided by the total number of paths (n). The total number of paths is the number of paths from each root node to each leaf node. while the depth is the total number of nodes starting with the root node, ending with the leaf node of one path. <math> D_j</math> is the total number of nodes on the path j.
<math>ADIT-LN= \frac{\sum D_j} {n} </math> ''for all'' <math> D_j </math> ''for'' <math> 1 \le j \le n</math>

[[Knowledgebase_Metrics#Sources | Source 2]]

==Sources==
#''Samir Tartir, I. Budak Arpinar, Michael Moore, Amit P. Sheth, and Boanerges Aleman-meza: Ontoqa: Metric-based ontology quality analysis. In: IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources, 2005, p 4. http://cobweb.cs.uga.edu/~budak/papers/ontoqa.pdf
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005 , pp 44-45. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf''

Knowledgebase Metrics

2016-09-07T10:33:20Z

Bl137:

The way data is placed within an ontology is also a very important measure of ontology quality because it can indicate the effectiveness of the ontology design and the amount of real-world knowledge represented by the ontology. Instance metrics include metrics that describe the knowledgebase as a whole, and metrics that describe the way each schema class is being utilized in the knowledgebase.

==Average Population==

(The average distribution of instances across all classes)

This measure is an indication of the number of instances compared to the number of classes. It can be useful if the ontology developer is not sure if enough instances were extracted compared to the number of classes.

Formally, the '''average population (AP)''' of classes in a knowledgebase is defined as the '''number of instances of the knowledgebase (I)''' divided by the '''number of classes defined in the ontology schema (C)'''.
<math>AP=\frac{|I|}{|C|}</math>

The result will be a real number that shows how well is the data extraction process that was performed to populate the knowledgebase. For example, if the average number of instances per class is low, when read in conjunction with the previous metric, this number would indicate that the instances extracted into the knowledgebase might be insufficient to represent all of the knowledge in the schema. Keep in mind that some of the schema classes might have a very low number or a very high number by the nature of what it is representing.

[[Knowledgebase_Metrics#Sources | Source 1]]

==Class Richness==

This metric is related to how instances are distributed across classes. The number of classes that have instances in the knowledgebase is compared with the total number of classes, giving a general idea of how well the knowledgebase utilizes the knowledge modelled by the schema classes. Thus, if the knowledgebase has a very low Class Richness, then the knowledgebase does not have data that exemplifies all the class knowledge that exists in the schema. On the other hand, a knowledgebase that has a very high class richness would indicate that the data in the knowledgebase represents most of the knowledge in the schema.

The '''class richness (CR)''' of a knowledgebase is defined as the percentage of the '''number of non-empty classes (classes with instances) (C')''' divided by the '''total number of classes (C)''' defined in the ontology schema.

<math>CR= \frac{|C'|}{|C|}</math>

[[Knowledgebase_Metrics#Sources | Source 1]]

==Cohesion==

The cohesion shows the degree of relatedness between the different entities. When the entities of an ontology are highly related there is a strong cohesion value.

To be able to measure the cohesion three different metrics will be used:

===Number of root classes (NoR)===
'''Same as Absolute Root Cardinality in Graph Metrics!!!'''

Displays the number of root classes of an ontology, a root class is a class which is not a sub class of any other class in the ontology. <math> C_j</math> is the jth root class.
<math>NoR= \sum C_j </math> ''for all'' <math>1 \le j \le n</math>
===Number of leaf classes (NoL)===
'''Same as Absolute Leaf Cardinality in Graph Metrics!!!'''

Displays the number of leaf classes of an ontology, a leaf class doesn't have any sub classes. <math> L_j</math> is the jth leaf class.

<math>NoL= \sum L_j </math> ''for all'' <math>1 \le j \le n</math>
===Average depth of inheritance tree of leaf nodes (ADIT-LN)===

It is the sum of the depth of all paths divided by the total number of paths (n). The total number of paths is the number of paths from each root node to each leaf node. while the depth is the total number of nodes starting with the root node, ending with the leaf node of one path. <math> D_j</math> is the total number of nodes on the path j.
<math>ADIT-LN= \frac{\sum D_j} {n} </math> ''for all'' <math> D_j </math> ''for'' <math> 1 \le j \le n</math>

[[Knowledgebase_Metrics#Sources | Source 2]]

==Sources==
#''Samir Tartir, I. Budak Arpinar, Michael Moore, Amit P. Sheth, and Boanerges Aleman-meza: Ontoqa: Metric-based ontology quality analysis. In: IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources, 2005, p 4. http://cobweb.cs.uga.edu/~budak/papers/ontoqa.pdf
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005 , pp 44-45. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf''

Knowledgebase Metrics

2016-09-07T10:24:36Z

Bl137:

The way data is placed within an ontology is also a very important measure of ontology quality because it can indicate the effectiveness of the ontology design and the amount of real-world knowledge represented by the ontology. Instance metrics include metrics that describe the knowledgebase as a whole, and metrics that describe the way each schema class is being utilized in the knowledgebase.

==Average Population==

(The average distribution of instances across all classes)

This measure is an indication of the number of instances compared to the number of classes. It can be useful if the ontology developer is not sure if enough instances were extracted compared to the number of classes.

Formally, the '''average population (AP)''' of classes in a knowledgebase is defined as the '''number of instances of the knowledgebase (I)''' divided by the '''number of classes defined in the ontology schema (C)'''.
<math>AP=\frac{|I|}{|C|}</math>

The result will be a real number that shows how well is the data extraction process that was performed to populate the knowledgebase. For example, if the average number of instances per class is low, when read in conjunction with the previous metric, this number would indicate that the instances extracted into the knowledgebase might be insufficient to represent all of the knowledge in the schema. Keep in mind that some of the schema classes might have a very low number or a very high number by the nature of what it is representing.

[[Knowledgebase_Metrics#Sources | Source 1]]

==Class Richness==

This metric is related to how instances are distributed across classes. The number of classes that have instances in the knowledgebase is compared with the total number of classes, giving a general idea of how well the knowledgebase utilizes the knowledge modelled by the schema classes. Thus, if the knowledgebase has a very low Class Richness, then the knowledgebase does not have data that exemplifies all the class knowledge that exists in the schema. On the other hand, a knowledgebase that has a very high class richness would indicate that the data in the knowledgebase represents most of the knowledge in the schema.

The '''class richness (CR)''' of a knowledgebase is defined as the percentage of the '''number of non-empty classes (classes with instances) (C')''' divided by the '''total number of classes (C)''' defined in the ontology schema.

<math>CR= \frac{|C'|}{|C|}</math>

[[Knowledgebase_Metrics#Sources | Source 1]]

==Cohesion==

The cohesion shows the degree of relatedness between the different entities. When the entities of an ontology are highly related there is a strong cohesion value.

To be able to measure the cohesion three different metrics will be used:

===Number of root classes (NoR)===
'''Same as Number of Roots in Graph Metrics!!!'''
Displays the number of root classes of an ontology, a root class is a class which is not a sub class of any other class in the ontology. <math> C_j</math> is the jth root class.
<math>NoR= \sum C_j </math> ''for all'' <math>1 \le j \le n</math>
===Number of leaf classes (NoL)===
Displays the number of leaf classes of an ontology, a leaf class doesn't have any sub classes. <math> L_j</math> is the jth leaf class.

<math>NoL= \sum L_j </math> ''for all'' <math>1 \le j \le n</math>
===Average depth of inheritance tree of leaf nodes (ADIT-LN)===

It is the sum of the depth of all paths divided by the total number of paths (n). The total number of paths is the number of paths from each root node to each leaf node. while the depth is the total number of nodes starting with the root node, ending with the leaf node of one path. <math> D_j</math> is the total number of nodes on the path j.
<math>ADIT-LN= \frac{\sum D_j} {n} </math> ''for all'' <math> D_j </math> ''for'' <math> 1 \le j \le n</math>

[[Knowledgebase_Metrics#Sources | Source 2]]

==Sources==
#''Samir Tartir, I. Budak Arpinar, Michael Moore, Amit P. Sheth, and Boanerges Aleman-meza: Ontoqa: Metric-based ontology quality analysis. In: IEEE Workshop on Knowledge Acquisition from Distributed, Autonomous, Semantically Heterogeneous Data and Knowledge Sources, 2005, p 4. http://cobweb.cs.uga.edu/~budak/papers/ontoqa.pdf
#''Aldo Gangemi, Carola Catenacci, Massimiliano Ciaramita, Jos Lehmann: Ontology evaluation and validation - An integrated formal model for the quality diagnostic task September 2005 , pp 44-45. http://www.loa.istc.cnr.it/old/Files/OntoEval4OntoDev_Final.pdf''